Senate Minority Leader Mitch McConnell said he will work to change an ineffective Senate: “We are going to function.”
Republicans made historic gains in Tuesday’s mid-term elections, gaining seats in the House of Representatives and capturing control of the Senate.
Mr Obama will respond later to what was a terrible result for Democrats.
“The Senate in the last few years basically doesn’t do anything,” Mr McConnell said on Wednesday. “We’re going to go back to work and actually pass legislation.”
“We’re going to go back to work and actually pass legislation”
He also vowed to “work together” with Mr Obama on issues where they can agree, such as trade agreements and tax reform.
Working within a two-party political system did not mean “we have to live in perpetual conflict”, he added.
Also on Wednesday, the chairman of the Republican National Committee called resounding Republican mid-term victories a “direct rejection of the Obama agenda”.
“[Americans] want nothing to do with the policies of Barack Obama,” Reince Priebus told reporters.
Rajesh Mirchandani explains what the results mean for Obama presidency
Barack Obama’s unpopularity in the run-up to these mid-term elections is hard to exaggerate. One of the things that is lost in the big picture of the night is some of the sidebar poll findings – the American people are fed up with all their politicians. It’s not just the occupant of the White House, though as Harry Truman most famously noted, the buck stops with the president.
Mitch McConnell will be conscious of that, and will know that in two years’ time, when it is not just the Senate but the presidency in play, the American people could be venting their spleen on him. Be fearful of the blame game.
That leaves the Kentucky senator with some important tactical decisions to make.
Throughout the campaign, Republicans focused on voter dissatisfaction with Mr Obama, a Democrat, describing the vote as a referendum on his presidency.
As the first results came in late on Tuesday, it became clear they had made the six gains they needed to win control of the Senate.
The Republicans won in Arkansas, Colorado, Iowa, Montana, North Carolina, South Dakota and West Virginia. The party now controls 52 seats, and is tipped to win at least one more as votes are counted in other states.
Their victory came on the back of a wave of discontent expressed by voters on the campaign trial – unhappy with an economic recovery they fail to feel the benefits of, and frustrated by political gridlock in Congress, which has already reached historic levels.
But echoing his successor’s sentiment of unity, current Senate Majority Leader Harry Reid congratulated Mr McConnell in a short statement.
“The message from voters is clear – they want us to work together,” said Mr Reid of Nevada, whose role in the soon-to-be Democratic minority remains uncertain.
“I look forward to working with Senator McConnell to get things done for the middle class.”
Winners and losers: “We are going to make them squeal”
The Republicans are also projected to increase their majority – by at least 10 seats – in the House of Representatives to levels not seen since before World War Two.
They also made gains among the 36 governorships up for re-election.
The Republicans will now have the power to complicate, if not block completely, Mr Obama’s agenda in the last two years of his tenure in the White House.
Control of the Senate will also enable the Republicans to stymie his ability to name new federal judges, cabinet members and senior government officials.
In the governor’s races, Republican incumbents survived some tough re-election battles and scored some surprising victories, cementing their success across several levels of government.
Voters approved ballot measures legalising cannabis in Oregon and Washington DC.
And three states – South Dakota, Arkansas and Nebraska – approved increases in the minimum wage. (BBC)
